Group-Equivariant Diffusion Models for Lattice Field Theory

Abstract:Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional $\phi^4$ and ${\rm U}(1)$ lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global $\mathbb{Z}_2$ reflections, local ${\rm U}(1)$ rotations, and periodic translations $\mathbb{T}$. The score networks are trained using an augmented training scheme, which significantly improves sample quality in the simulated field theories. We also demonstrate empirically that our symmetry-aware models outperform generic score networks in sample quality, expressivity, and effective sample size.

Updated to match published version in JHEP. 45 pages, 12 figures. Code available at this https URL

High Energy Physics - Lattice (hep-lat); Machine Learning (cs.LG)

arXiv:2510.26081 [hep-lat]

(or arXiv:2510.26081v2 [hep-lat] for this version)

https://doi.org/10.48550/arXiv.2510.26081 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1007/JHEP07%282026%29213 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.